An existence and uniqueness theorem for Conjecture REF  was given, for complete metrics on the sphere minus a finite number of disks, in [1]}. A dual statement proving Conjecture REF  for complete metrics on the sphere minus a finite number of disks was also given in [1]}. Seen in this manner, the Geometric Koebe Conjecture appears as an instance of the Weyl problem in hyperbolic space, and it is tempting to assume that a similar statement extends to metrics of variable curvature, see [3]}.
